Semi-additive functionals of semi-Markov processes and measure-valued Poisson equation

Shanshan Liu, Xiaoyu Xing and Guoxin Liu

Statistics & Probability Letters, 2019, vol. 147, issue C, 45-56

Abstract: In this paper, we consider a continuous-time semi-Markov process (SMP) in Polish spaces. We first introduce the semi-additive functional in semi-Markov cases, a natural generalization of the additive functional of Markov process (MP). The main contribution of this paper is the properties of semi-additive functional aforementioned. First, semi-additive functionals of SMPs are characterized in terms of a càdlàg function with zero initial value and a measurable function. Second, the necessary and sufficient conditions are investigated under which a semi-additive functional of SMP is a semimartingale, a local martingale, or a special semimartingale respectively. By the way, the Itô type formula is given. Finally, we study the expected cumulative discounted value of the semi-additive functional of an SMP. We prove that it solves a measure-valued Poisson equation and give the uniqueness conditions.

Keywords: Semi-Markov process; Semi-additive functional; Itô formula; Expected cumulative discounted value; Measure-valued Poisson equation (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715218303511
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:147:y:2019:i:c:p:45-56

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2018.11.004

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().